cfd prediction of turbulent flow on an experimental tidal...
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1st Asian Wave and Tidal Conference Series
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NOMENCLATURE
A
𝐶𝑇 𝑃⁄
𝐶̅
�̃�
𝐶′
𝐶∗
𝐶𝜇
𝐼
𝑘
𝐿
𝑅
TSR
𝑈0
𝑦+
𝜀
𝜌
𝜙𝑖
𝜔
Ω
= Swept area of turbine (m2)
= Thrust (T) / Power (P) coefficients
= Time-averaged coefficient
= Phase-averaged coefficient
= RMS of 𝐶̅
= RMS of �̃�
= Constant
= Turbulent intensity
= Turbulent kinetic energy (m2s-2)
= Turbulent length scale (m)
= Turbine blade radius (m)
= Tip-speed-ratio
= Inflow velocity (ms-1)
= Non-dimensional wall distance of mesh
= Turbulent dissipation rate (m2 s-3)
= Fluid density (kg m-3)
= Value of variable 𝜙 at cell 𝑖
= Specific rate of turbulent dissipation (s-1)
= Angular velocity of turbine (rad s-1)
1. Introduction
Interest in renewable energy has come into the forefront over the
last decade due to concerns of diminishing oil and coal supplies as
well as from worldwide political pressures to “go green”. Tidal
currents provide the opportunity to extract energy from a powerful
and predictable resource. One method of energy extraction from tidal
currents is to use a tidal stream turbine (TST). A report by the
European Commission (1996) identified numerous tidal sites with an
estimated power rating exceeding 10MW per square km. The
Orkneys, off the north coast of Scotland, are among these power-rich
sites and home to the European Marine Energy Centre (EMEC).
Osalusi et al. (2009) show that currents at the EMEC test site are
highly turbulent with mean velocities greater than 1m/s, meaning
TSTs experience strong and unsteady loading. To understand the
effect of such flow-features, experimental and computational studies
are used. Bahaj et al. (2005, 2007) present a study of flow past an
experimental TST in a towing tank and cavitation tunnel presenting
the thrust and power coefficients, 𝐶𝑇, and 𝐶𝑃 respectively, against
the tip-speed ratio (TSR), which are defined as:
TSR =Ω𝑅
𝑈0
CFD Prediction of Turbulent Flow on an Experimental Tidal Stream Turbine using RANS modelling
James McNaughton1,#, Stefano Rolfo1, David Apsley1, Imran Afgan1,2, Peter Stansby1 and Tim Stallard1
1 School of Mechanical Aerospace and Civil Engineering, University of Manchester, Sackville Street, Manchester, M1 3BB, England 2 Institute of Avionics & Aeronautics, Air University, E-9, Islamabad, Pakistan
# Corresponding Author / E-mail: [email protected], TEL: +44-7772-533014
KEYWORDS : Computational Fluid Dynamics (CFD), Reynolds Averaged Navier Stokes (RANS), Tidal energy, Tidal stream turbine (TST), ReDAPT
A detailed computational fluid dynamics (CFD) study of a laboratory scale tidal stream turbine (TST) is presented. Three separate Reynolds
Averaged Navier Stokes (RANS) models: the 𝑘 − 𝜀 and 𝑘 − 𝜔 SST eddy-viscosity models, and the Launder-Reece-Rodi (LRR) Reynolds
stress model, are used to simulate the turbulent flow-field using a new sliding-mesh method implemented in EDF's open-source
Computational Fluid Dynamics solver, Code_Saturne. Validation of the method is provided through a comparison of power and thrust
measurements for varying tip-speed ratios (TSR). The SST and LRR models yield results within several per cent of experimental values,
whilst the k-ε model significantly under-predicts the force coefficients. The blade and turbine performance for each model is examined to
identify the quality of the predictions. Finally, detailed modelling of the turbulence and velocity in the near and far wake is presented. The
SST and LRR models are able to identify tip vortex structures and effects of the mast as opposed to the standard 𝑘 − 𝜀 model.
1st Asian Wave and Tidal Conference Series
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𝐶𝑇 =Thrust12𝜌𝐴𝑈0
2
𝐶𝑃 =Power12𝜌𝐴𝑈0
3
Where Ω is the angular velocity of the TST in rad/s, R is the blade
radius (m), 𝑈0 is the reference velocity (m s-1), 𝜌 is the fluid
density (kg m-3) and 𝐴 = 𝜋𝑅2 is the swept area of the turbine (m2).
Whilst these studies provide a large data set for the mean force
coefficients, they provide little information about the behaviour in the
wake. Indeed, experimentally it is hard to observe the fluid behaviour
close to the turbine and therefore modelling can provide further
insight in these areas. Blade element / momentum (BEM) methods,
originally used in wind-turbine design (Wilson & Lissaman, 1974),
divide blades into 2D sections for which drag and lift coefficients are
known. BEM methods have been used in TST modelling (eg Batten
et al. 2008) with results comparable to experimental values. However,
BEM is unable to model the more complex flow conditions and
reveals no information of unsteady loading or the wake.
Computational fluid dynamics (CFD) is a valuable tool that
allows these gaps to be bridged. One common method for CFD
analysis of TSTs uses actuator disk theory. In this method the TST is
modelled as a porous disk that inflicts a pressure drop as fluid passes
through it (eg Gant and Stallard, 2008). Such a method is useful in
predicting the far wake, but gives little information close to the
turbine, as shown by Harrison et al., (2009). Detailed CFD modelling
of Bahaj et al.’s TST is demonstrated by McSherry et al. (2011) and
Afgan et al. (2012), which model the turbine’s blades and support
structure. The first of these studies uses Reynolds Averaged Navier
Stokes (RANS) modelling to represent the turbulence, whilst the
latter uses Large Eddy Simulation (LES), with both studies predicting
power and thrust measurements close to the experimental data. LES is
a more computationally expensive method but provides a greater
level of detail than RANS. Indeed, the computational mesh used by
Afgan et al. has over twenty times more cells than that of McSherry et
al.’s and the increase in CPU time is in the order of 100,000’s.
However, whilst the RANS study only provides details of the power
and thrust measurements, the LES provides detailed information in
the near wake and on the blade surfaces.
This paper addresses the gap left between the RANS and LES
calculations of a TST that are described above. A sliding-mesh
method is used to model detailed flow past the experimental model of
Bahaj et al.’s horizontal-axis TST. Simulations using this geometry
are used to assess the suitability of different RANS models with
comparisons drawn with the LES of Afgan et al. where applicable.
2. Methodology
2.1. Numerical Solver
Simulations are performed using Électricité de France Research
and Development’s (EDF R&D) open-source CFD solver,
Code_Saturne (Archambeau, 2004). The code is an unstructured
finite volume-code using pressure-velocity coupling through a
predictor-corrector scheme. The code is optimised for large parallel
calculations (Fournier et al., 2011). Second-order-slope-limited
differencing is used in space and first-order implicit Euler scheme is
used in time.
2.2. Turbulence models
Three different RANS models are selected for validation of
results with the Southampton turbine: the 𝑘 − 𝜀 (Launder & Sharma,
1974) and 𝑘 − 𝜔 SST (Menter, 1994) eddy-viscosity models and the
Launder-Reece-Rodi (LRR, see Launder et al., 1975) Reynolds Stress
Model (RSM). These models are popular, often chosen as industry
standards, and typical of those used by previous studies of TSTs (e.g.
Mason Jones et al., 2008, O’Doherty et al., 2009, Harrison et al.,
2009). RSMs are able to model anisotropy by solving separate
transport equations for each of the Reynolds stresses whilst eddy-
viscosity models cannot achieve this as they assume that the Reynolds
Stress tensor is proportional to the mean strain rate. For this reason it
is often observed (for example in Wilcox, 1994) that eddy-viscosity
models are not suitable for predicting flows with rotation or strong
curvature effects as is expected in the current flow.
2.3. Wall functions
Due to the complex nature of both flow and geometry it is
difficult to obtain a near wall cell that is well placed within the
laminar sub-layer (i.e. at 𝑦+ ≈ 1, where 𝑦+ is the dimensionless
wall-distance) which is a necessary condition to correctly resolve the
boundary layer. Therefore wall-functions are used based on the
classical log-law (von Kármán, 1930) with the modification proposed
by Grotjans & Menter (1998), known as the scalable wall-function.
The advantage of this formulation is that the near wall distance is
prevented from falling below a set limit (in Code_Saturne this is set
at 10.88) so that the near wall cell-centre always lies within the buffer
layer, and hence the wall-function’s requirements are always satisfied.
2.4. Boundary conditions
To recreate the conditions of the towing tank, slip boundary
conditions are placed on the sides, top and bottom walls of the
domain. The turbine and its support have no-slip walls. The inlet has a
uniform velocity profile with a fixed turbulence intensity of 𝐼 = 1%.
The turbulent kinetic energy (TKE), 𝑘, and dissipation rate, 𝜀, are
defined at the inlet:
𝑘 = 3
2(𝐼𝑈0)
2
𝜀 = 𝐶𝜇
34 𝑘
32
𝐿
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𝐶𝜇 = 0.09 is a constant and 𝐿 is the turbulent length scale that is
given the value of 0.7 times the turbine hub-height, as described in
Gant and Stallard (2007). For the 𝑘 − 𝜀 model these values are
prescribed at the inlet whilst for the other models they are used to
calculate the required variables from their definitions.
2.5. Sliding mesh
In order to rotate the turbine the mesh is created as two blocks: an
outer-stationary and an inner-rotating part. A sliding-mesh approach is
developed within Code_Saturne as part of this work. The sliding-
mesh interface employs an internal Dirichlet boundary condition
calculated from a halo-node as in Fig. 1. The value of any variable,
𝜙, at face, 𝐹, on the sliding-mesh interface is given the value 𝜙𝐹:
𝜙𝐹 = 𝜙𝐴 + 𝜙𝐻
2
Where 𝐴 is the cell connected to 𝐹 and 𝐻 is the halo-point; found
by reflecting 𝐴 through 𝐹. The value at 𝐻 is found by
extrapolating from the nearest cell-centre, 𝐵, say:
𝜙𝐻 = 𝜙𝐵 + ∇𝜙𝐵 ∙ 𝐵𝐻⃗⃗⃗⃗⃗⃗
2.6. Geometry
The turbine is a 0.8m diameter experimental model whose blades
are constructed from seventeen NACA 6-series aerofoil profiles that
change in pitch, chord-length and thickness along the blade radius, 𝑅.
The profiles and all other geometry such as the support are defined in
Bahaj et al. (2005). A block-structured mesh is used entirely
throughout the geometry. A c-mesh is used around the blades as in Fig.
2a. The trailing edges of each profile have been thickened using a
function described in Herrig et al. (1951) to allow for a more realistic
blade design, as well as allowing for the structured mesh at the blade-
tip. The near-wall spacing of the mesh is designed to give a 𝑦+ value
in the range 15-300 which are suitable for wall-functions. If the value
of 𝑦+ falls below 10.88 the scalable wall-function is activated.
The turbine is created in a 120° segment as shown in Fig. 2b and
then copied twice around the axis of rotation to create a cylindrical
block. This block is housed inside an outer domain shown in Fig. 2c
with the turbine and outer blocks communicating via a sliding-mesh
method described in Sec. 2.5. The domain matches the depth and
breadth of the towing tank in Bahaj et al. (2005) with the inlet 5D
upstream of the turbine and the outlet 12D downstream.
2.7. Mesh refinement
Convergence of the solution is sought for three levels of meshing
(coarse, medium, fine) for the turbine block and two (medium, fine)
for the outer domain. These are described in Table 1 alongside the
mean thrust and power coefficients obtained using the 𝑘 − 𝜔 SST
model with TSR=6. The fine turbine block changes these values by
less than one percent and so this level of refinement is not deemed
necessary here and the medium mesh is used. Refining the outer
domain again has a negligible effect on the coefficients, implying that
this level of refinement in the domain is not necessary to match the
force coefficients of the experiments. The effect in the downstream
wake is shown by mean velocity profiles in the wake in Fig. 3. At 1D
no significant differences are seen between the solutions although the
finer mesh identifies more variation in the centre-line of the turbine.
At 5D the difference between solutions is again negligible although
by 10D the coarser solution has shown a greater wake recovery by
around 10% on the centre-line. Hence for studying the wake
confidence can be drawn in the near wake solution but further
downstream there may be errors arising from the mesh. The
simulations use a time-step equivalent to 0.6° of rotation per time-step.
Although this is quite low, doubling the time-step affects these results
by approximately 8% and so cannot be increased without
significantly effecting results.
Table 1 Mean force coefficients for different sizes of meshes.
Mesh No cells
turbine
No cells
domain
No cells
total
𝐶𝑇 𝐶𝑃
Coarse 823977 627356 1451333 0.8094 0.4446
Medium 3078636 627356 3705992 0.8270 0.4638
Fine 5336976 627356 5964332 0.8256 0.4651
Medium w/
fine outer
3078636 2395928 5474564 0.8278 0.4635
(a) C-mesh (green) and tip mesh (red). (b) 120° segment. (c) Outline of domain.
Figure 2. Overview of domain and mesh. Figure 1. Interpolation of cells
for sliding mesh method.
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Figure 3. Mean velocity profiles for medium and fine outer domain meshes.
1D 5D 10D
3. Results
Simulations are performed using the University of Manchester’s
Computational Shared Facility (CSF) with each simulation running
on between 32 and 128 cores and taking approximately 20,000 CPU
hours for the force coefficients to reach a periodic state. The 𝑘 − 𝜀 is
the least expensive model to run computationally, with the LRR and
𝑘 − 𝜔 SST models taking approximately two and three times longer,
respectively. This is expected for the LRR model which solves
transport equations for the Reynolds stresses, whilst the high cost of
the SST can be attributed to the requirement to calculate the wall
distance at each time-step. To reduce computational cost for the
parametric test of TSRs, each simulation is performed in turn
restarting from the previous results. The time step is adjusted to give
the same angle of rotation per time step. Once a periodic state is
achieved for each TSR the calculation is allowed to run for a
minimum of three further complete rotations. For further analysis of
the optimal TSR these results are averaged over a time corresponding
to the fluid travelling from the turbine to the outlet
Fig. 4 shows the instantaneous velocity flow-field for the three
models at TSR=6 all captured at approximately the same instant. The
SST and LRR models show quite unsteady wakes, especially behind
the mast, with the SST model capturing a larger area of recirculation
behind the top of the mast. Similarly the velocity deficit from the tip
vortices are visible in all three instances, although the
capture this as well as the other models. The simulations take
approximately 7 seconds of physical time before reaching a periodic
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Figure 6. Phase averaging of power coefficient over one rotation. (a) Instantaneous values and their phase average. Normalised phase
average of thrust (b) and power (c) for different RANS models.
(a) (b) (c)
close to the experimental data curves, with the worst agreement at the
lowest TSR. Both these models show results within several per cent
of the LES, under predicting the 𝐶𝑃 values slightly but giving better
agreement to the experiments for the thrust coefficient.
3.2. Performance characteristics
A better understanding of the different turbulence models’
performances is given by the force coefficient behaviour throughout
each rotation. Fig. 6a shows several sets of the instantaneous power
coefficient plotted over a single rotation. Defining the phase as this
time interval, then the phase average, 𝐶�̃�, is obtained by averaging
the data points that are at the same point in the phase. Fig. 6b and c
also show the normalised phase averaged thrust and power
coefficients, 𝐶�̃�/𝐶𝑃 and 𝐶�̃�/𝐶𝑃 respectively, for each of the RANS
models. All models experience larger fluctuations for power than
thrust indicating a larger unsteadiness for the rotational effects.
Further to this there are two frequencies identifiable for each model:
the larger of these occurring at the point where a blade is directly in
front of the mast, indicated by the zero, one- and two-third points of
the phase. For the SST and LRR models interaction with the mast is
thus indicated by the maximum and minimum peaks of the
coefficients occurring before and after each blade passing respectively.
Compared to the LRR models these peaks are smaller for the SST
model and are delayed slightly. The 𝑘 − 𝜀 model predictions are
delayed even further, placing it almost in anti-phase to the LRR
model, hence predicting maximum values after a blade passes the
mast. Whilst the 𝑘 − 𝜀 and LRR models predict a steady oscillatory
motion for their peaks and troughs the SST shows a recovery and stall
in the 𝐶�̃� and 𝐶�̃� peaks respectively as each blade passes the mast.
This shows the SST is predicting a secondary interaction with the
mast. Indeed, referring back to Fig. 4 the velocity gradient extending
from the join between the mast and the nacelle is greater for the SST
model than the other turbulence closures.
Root mean square (RMS) fluctuations of each coefficient from
the mean, 𝐶𝑃′ , and from the phase, 𝐶𝑃
∗, are defined as:
𝐶𝑃′ = √(𝐶𝑃 − 𝐶𝑃 )
2
𝐶𝑃∗ = √(𝐶𝑃 − 𝐶�̃�)
2
These are given in Table 2 which shows the fluctuations from the
phase to be around half that of those from the mean for all models
identifying that even with this well-defined phase the unsteadiness of
the solution is still large. The LRR model’s predictions of these
fluctuations are almost twice that of the SST and over double the
𝑘 − 𝜀 model’s values. This behaviour may be due to RSMs tending
to naturally damp the modelling contribution which allows for a
larger amount of the turbulent spectrum to be resolved. This is again
observed in the comparison between TKE and resolved velocity
Figure 5. Blockage corrected thrust and power coefficients for
different RANS models compared to experimental data.
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fluctuations detailed in Sec. 3.3. Whilst the SST is able to accurately
predict the mean flow this shows an advantage of the LRR for
examining unsteady loads.
A greater understanding of the loading on the blades is obtained
from the mean pressure coefficient:
𝐶�̅�𝑟𝑒𝑠 =𝑝 − 𝑝𝑟𝑒𝑓12𝜌𝑈0
2
𝑝𝑟𝑒𝑓 is the reference pressure taken at the centre point of the inflow
boundary. 𝐶�̅�𝑟𝑒𝑠 is shown at one-quarter lengths along the blade in
Fig. 7 as a function of distance, 𝑐, along chord length, 𝐶. The large
variation in the pressure coefficient from root (r/R=0.25) to tip
(r/R=0.75) is due to the normalisation only taking into account the
inflow velocity as opposed to using the relative velocity based on Ω𝑟,
in this manner a better understanding of the forces at each section are
given in relation to each other as well as between models. The 𝑘 − 𝜀
model shows quite different performance characteristics to the other
models, this is a direct result of the model’s insensitivity to adverse
pressure gradients and curvature. At one quarter radius this is
observed by the inability to maintain the large suction peak at the
leading edge and thus the pressure recovery is quite steep. This
characteristic is seen for the other presented sections although is less
severe.
The plots at r/R=0.5 exhibit separation for all models in the
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for the tidal industry.
The purpose of this work is to identify suitable methodology and
RANS models for analysis of Tidal Generation Ltd’s 1MW TST that
is installed at EMEC. The flow speeds used for the experiment are
similar to those of the EMEC test site; hence the Reynolds number
will increase linearly with the increase in diameter. Full-scale devices
are also subject to substantial velocity shear, greater turbulence
intensities and wave-induced fluctuations. Future work will
investigate these effects using the methods described here.
ACKNOWLEDGEMENT
This research was performed as part of the Reliable Data